The quarrel between the TV host and first daughter began after she tweeted: 'FACT: Greenhouse gases generated by the U.S. will slide 9.2% this year, tumbling to the lowest level in at least three decades.'
Tapper replied to the White House adviser to say: 'This is largely because of the pandemic and the economic catastrophe it wrought.' He then shared a link to a Washington Post article on the issue, writing: '2/ Kind of an important detail.'
But when she hit back, telling him the emissions were declining in 2019 before the pandemic, Tapper was forced to concede, this time arguing market forces were at play and not policy.
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On Twitter, pro-Trump users noted that is 'awesome'; another said 'Capitalism wins again.'
President Trump, who has worked to undo most of Barack Obama's efforts to fight climate change, again railed against the Paris climate accord on Sunday. The U.S. exited the Paris pact on November 4, a decision Trump has faced criticism for.
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Trump alleged to world leaders at a virtual summit that the agreement was designed to cripple the U.S. economy, not save the planet.
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'To protect American workers, I withdrew the United States from the unfair and one-sided Paris climate accord, a very unfair act for the United States,' Trump said.
President-elect Joe Biden, who takes office in January, has said he will rejoin the global pact that the U.S. helped forge five years ago.
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Following the Twitter spat a number of users - including Trump supporters - claimed it as evidence that the private sector had 'dealt' with the problem 'better than giant globalist accords'.
However, with its giant economy, the U.S. has far more raw emissions of climate-damaging carbon dioxide to cut than any other country except China.
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A more telling measure of progress in various countries is the percentage of emissions a county has cut. Since 2005, the United States hasn't been even in the top 10 in percentage of greenhouse gas emission reductions.
The main drivers of carbon emissions are transportation, at 28%, electricity, at 27%, and industry at 22% of all emissions.
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Over the past decade coal-fired power stations have closed rapidly, with natural gas and renewables use increasing rapidly.
Transport emissions had ticked up under Trump, continuing a trend which began in 2011 and is broadly in line with economic growth.
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Most transport emissions are from cars and light trucks, making them highly responsive to the state of the economy. Manufacturers, however, have increased efficiency so the 2019 fall could be due to economic growth of 2.3% - far below the 4% promised by Trump - and increased efficiency combining to generate lower emissions.
Scientists say that any rise beyond 2 degrees Celsius would have a devastating impact on large parts of the world, rising sea levels, stoking tropical storms and worsening droughts and floods.